Question

Select the correct prime factorization of 54.

• A. 3 × 18
• B. 2 × 27
• C. 2 × 3 × 3 × 3
• D. 6 × 9

Answer 1

The correct option is C 2 × 3 × 3 × 3

Let's solve this using factor tree method


Factors of 54 by prime factorization are given by the following steps.

Step 1: Write the pair of factors, which on multiplication gives the required number.
54 = 2 × 27

Step 2: See the factors, whether each one of them is prime or not.

27 is not a prime number and can be dissociated as a product of 3 by 9.

9 is not a prime number and can be dissociated as a product of 3 and 3.

Step 3: As per the criteria, 54 can be written as 54 = 2 × 27
= 2 × 3 × 9
= 2 × 3 × 3 × 3.

So, prime the factorization of 54
= 2 × 3 × 3 × 3.
= $2\times 3^3$